Hiromasa Tamae’s research while affiliated with The University of Tokyo and other places

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Publications (8)


Score-adjusted methods for estimation of shape parameters in Gamma-Poisson and Beta-Binomial distributions
  • Article

February 2022

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7 Reads

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3 Citations

Communication in Statistics- Simulation and Computation

Hiromasa Tamae

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Kaoru Irie

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Tatsuya Kubokawa

The gamma-Poisson and beta-binomial mixture distributions are used for analyzing count-valued data, and the estimation of the hyper-parameters including the shape and/or scale parameters is important in the empirical Bayes inference. The maximum likelihood method requires the nested loops for solving the non-linear equations at each step of iteration in the EM algorithm. To avoid the extra loops, we derive the closed-form updating procedures at each step of iteration by using the score-adjusted method. The performance is compared by simulation with the maximum likelihood estimators.


General unbiased estimating equations for variance components in linear mixed models

September 2021

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22 Reads

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2 Citations

Japanese Journal of Statistics and Data Science

This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator. We derive the asymptotic covariance matrices and second-order biases under general estimating equations without assuming the normality of the underlying distributions and identify a class of second-order unbiased estimators of variance components. It is also shown that the asymptotic covariance matrices and second-order biases do not depend on whether the regression coefficients are estimated by the generalized or ordinary least squares methods. We carry out numerical studies to check the performance of the proposed methods based on typical linear mixed models.


General Unbiased Estimating Equations for Variance Components in Linear Mixed Models

May 2021

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25 Reads

This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator. We derive the asymptotic covariance matrices and second-order biases under general estimating equations without assuming the normality of the underlying distributions and identify a class of second-order unbiased estimators of variance components. It is also shown that the asymptotic covariance matrices and second-order biases do not depend on whether the regression coefficients are estimated by the generalized or ordinary least squares methods. We carry out numerical studies to check the performance of the proposed method based on typical linear mixed models.


Predicting intervention effect for COVID-19 in Japan: state space modeling approach

May 2020

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97 Reads

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45 Citations

Bioscience Trends

Japan has observed a surge in the number of confirmed cases of the coronavirus disease (COVID-19) that has caused a serious impact on the society especially after the declaration of the state of emergency on April 7, 2020. This study analyzes the real time data from March 1 to April 22, 2020 by adopting a sophisticated statistical modeling based on the state space model combined with the well-known susceptible-infected-recovered (SIR) model. The model estimation and forecasting are conducted using the Bayesian methodology. The present study provides the parameter estimates of the unknown parameters that critically determine the epidemic process derived from the SIR model and prediction of the future transition of the infectious proportion including the size and timing of the epidemic peak with the prediction intervals that naturally accounts for the uncertainty. Even though the epidemic appears to be settling down during this intervention period, the prediction results under various scenarios using the data up to May 18 reveal that the temporary reduction in the infection rate would still result in a delayed the epidemic peak unless the long-term reproduction number is controlled.


Predicting Infection of COVID-19 in Japan: State Space Modeling Approach

April 2020

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120 Reads

The number of confirmed cases of the coronavirus disease (COVID-19) in Japan has been increasing day by day and has had a serious impact on the society especially after the declaration of the state of emergency on April 7, 2020. This study analyzes the real time data from March 1 to April 22, 2020 by adopting a sophisticated statistical modeling tool based on the state space model combined with the well-known susceptible-exposed-infected (SIR) model. The model estimation and forecasting are conducted using the Bayesian methodology. The present study provides the parameter estimates of the unknown parameters that critically determine the epidemic process derived from the SIR model and prediction of the future transition of the infectious proportion including the size and timing of the epidemic peak with the prediction intervals that naturally accounts for the uncertainty. The prediction results under various scenarios reveals that the temporary reduction in the infection rate until the planned lifting of the state on May 6 will only delay the epidemic peak slightly. In order to minimize the spread of the epidemic, it is strongly suggested that an intervention is carried out for an extended period of time and that the government and individuals make a long term effort to reduce the infection rate even after the lifting.


A score-adjusted approach to closed-form estimators for the gamma and beta distributions

January 2020

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14 Reads

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11 Citations

Japanese Journal of Statistics and Data Science

The closed-form estimators proposed by Ye and Chen (Am Stat 71(2):177–181, 2017) for the gamma distribution can be derived by the score-adjusted method, and in the orthogonal reparameterization, the asymptotic variances are compared with the maximum likelihood and moment estimators. This method is also useful for providing closed-form estimators for the beta distribution.


Small Area Predictors with Dual Shrinkage of Means and Variances

July 2015

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25 Reads

The paper concerns small-area estimation in the Fay-Herriot type area-level model with random dispersions, which models the case that the sampling errors change from area to area. The resulting Bayes estimator shrinks both means and variances, but needs numerical computation to provide the estimates. In this paper, an approximated empirical Bayes (AEB) estimator with a closed form is suggested. The model parameters are estimated via the moment method, and the mean squared error of the AEB is estimated via the single parametric bootstrap method. The benchmarked estimator and a second-order unbiased estimator of the mean squared error are also derived.


Bayesian Estimators for Small Area Models Shrinking Both Means and Variances

July 2015

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64 Reads

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37 Citations

Scandinavian Journal of Statistics

For small area estimation of area-level data, the Fay-Herriot model is extensively used as a model based method. In the Fay Herriot model, it is conventionally assumed that the sampling variances are known whereas estimators of sampling variances are used in practice. Thus, the settings of knowing sampling variances are unrealistic and several methods are proposed to overcome this problem. In this paper, we assume the situation where the direct estimators of the sampling variances are available as well as the sample means. Using these information, we propose a Bayesian yet objective method producing shrinkage estimation of both means and variances in the Fay-Herriot model. We consider the hierarchical structure for the sampling variances and we set uniform prior on model parameters to keep objectivity of the proposed model. For validity of the posterior inference, we show under mild conditions that the posterior distribution is proper and has finite variances. We investigate the numerical performance through simulation and empirical studies.

Citations (4)


... The second extension is best described in Tamae et al. (2020), which highlighted that the Generalized Gamma distribution or any other transformation is not necessary, since the estimators of Ye & Chen (2017) are in fact moment-type estimators that can be derived by equating E(X) = αβ and C(X, log X) = β to their sample counterparts. The authors called these the score-adjusted moment estimators (SAME) and applied this methodology to derive closed-form estimators for the parameters of the Beta, Gamma-Poisson, and Beta-Binomial distributions (Tamae et al. 2020(Tamae et al. , 2022. However, it's important to note that in the case of the Gamma distribution, these estimators were originally derived by Wiens et al. (2003), who used the same methodology as Tamae et al. (2020), except for the fact that the sample covariance set equal to C(X, log X) was the unbiased one (dividing by n − 1 instead of n). ...

Reference:

Moment-Type Estimators for the Dirichlet and the Multivariate Gamma Distributions
Score-adjusted methods for estimation of shape parameters in Gamma-Poisson and Beta-Binomial distributions
  • Citing Article
  • February 2022

Communication in Statistics- Simulation and Computation

... State space methods and regime-switching models have gained popularity in the analysis of complex time series data and have demonstrated potential in examining individual health records [Guo et al., 1999, Guo and Brown, 2000, Liu et al., 2014, Samdin et al., 2017, Noman et al., 2020. Numerous studies have utilized these methods to investigate intervention effects [Kobayashi et al., 2020], forecast outcomes [Petrica et al., 2022, O'Dea and Drake, 2022, Noh et al., 2023, track disease transmission [Zhou and Ji, 2020, Deo and Grover, 2021, Keller et al., 2022, and explore other socioeconomic factors related to COVID-19 at the population level [Shah et al., 2021]. However, methods for detecting change points at the individual level remain limited. ...

Predicting intervention effect for COVID-19 in Japan: state space modeling approach
  • Citing Article
  • May 2020

Bioscience Trends

... There are a number of different methodological proposals in the literature for obtaining closeform estimators; see, for example, the moment-based type (Cheng and Beaulieu, 2002) and the score-adjusted approaches (Nawa and Nadarajah, 2023;Tamae et al., 2020). Closed-form estimators based on the likelihood function have also been suggested. ...

A score-adjusted approach to closed-form estimators for the gamma and beta distributions
  • Citing Article
  • January 2020

Japanese Journal of Statistics and Data Science

... Sugasawa and Kubokawa, 2020). Notably, Sugasawa et al. (2017) and Gene Hwang et al. (2009) employed random-effects models for both means and variance to achieve stable variance estimation under small sample sizes, resulting in accurate mean estimation. Such approaches are partially adopted in meta-analysis (e.g. ...

Bayesian Estimators for Small Area Models Shrinking Both Means and Variances
  • Citing Article
  • July 2015

Scandinavian Journal of Statistics